Bernhard Holzer

Introduction to Longitudinal Beam Dynamics

This chapter gives an overview of the longitudinal dynamics of the particles in an accelerator and, closely related to that, of the concept of synchronization between the particles and the accelerating field. Beginning with the trivial case of electrostatic accelerators, the synchronization condition is explained for a number of driven accelerators like Alvarez linacs, cyclotrons and finally synchrotrons and storage rings, where it plays a crucial role. In the case of the latter, the principle of phase focusing is motivated qualitatively as well as on a mathematically more correct level and the problem of operation below and above the transition energy is discussed. Throughout, the main emphasis is more on physical understanding rather than on a mathematically rigorous treatment.

CAS - CERN Accelerator School: Plasma Wake Acceleration

These proceedings are of interest to staff and students in accelerator laboratories, university departments and companies working in or having an interest in the field of new acceleration techniques. Following introductory lectures on plasma and laser physics, the course covers the different components of a plasma wake accelerator and plasma beam systems. Topical seminars and an overview about alternative new techniques like dielectric accelerators are included. Lectures on the experimental studies and their latest results, on diagnostic tools and state of the art wake acceleration facilities, both present and planned, complement the theoretical part.

Status of the 11 T Nb

The planned upgrade of the LHC collimation system includes additional collimators in the LHC lattice. The longitudinal space for the collimators could be obtained by replacing some LHC main dipoles with shorter but stronger dipoles compatible with the LHC lattice and main systems. A joint development program with the goal of building a 5.5 m long two-in-one aperture Nb3Sn dipole prototype suitable for installation in the LHC is being conducted by FNAL and CERN magnet groups. As part of the first phase of the program, 1 m long and 2 m long single aperture models are being built and tested, and the collared coils from these magnets will be assembled and tested in two-in-one configuration in both laboratories. In parallel with the short model magnet activities, the work has started on the production line in view of the scale-up to 5.5 m long prototype magnet. The development of the final cryo-assembly comprising two 5.5 m long 11 T dipole cold masses and the warm collimator in the middle, fully compatible with the LHC main systems and the existing machine interfaces, has also started at CERN. This paper summarizes the progress made at CERN and FNAL towards the construction of 5.5 m long 11 T Nb3Sn dipole prototype and the present status of the activities related to the integration of the 11 T dipole and collimator in the LHC.

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In this chapter we give an introduction to the transverse dynamics of the particles in a synchrotron or storage ring. The emphasis is more on qualitative understanding rather than on mathematical correctness, and a number of simulations are used to demonstrate the physical behaviour of the particles. Starting from the basic principles of how to design the geometry of the ring, we review the transverse motion of the particles, motivate the equation of motion, and show the solutions for typical storage ring elements. Following the usual treatment in the literature, we present a second way to describe the particle beam, using the concept of the emittance of the particle ensemble and the beta function, which reflects the overall focusing properties of the ring. The adiabatic shrinking due to Liouvilles theorem is discussed as well as dispersive effects in the most simple case.

Sn Dipole Project for the LHC

The Large Hadron Electron Collider (LHeC) project is a proposal for high luminosity TeV-scale electron–proton (ep) collisions at the LHC. The LHeC Conceptual Design Report presented an early overview of the machine, including an electron linac solution and a solution involving a 60 GeV electron storage ring. Here we present a new complete solution for the collision insertion of this electron ring, incorporating all constraints including those imposed by the LHC and, for the first time, proving the feasibility of ep collisions at a luminosity of ∼1033 cm−2s−1 in the LHC era. The solution presented offers high luminosity while maintaining the large detector coverage required by the particle physics programme. This negates the earlier need for two separate interaction region designs, one optimized for high luminosity at the cost of detector coverage, and the other for lower luminosity but higher coverage. Synchrotron radiation emission is also a major factor in electron accelerator design, and studies are presented showing the feasibility of the design in this regard. The design is found to be technically viable, solving the problem of TeV-scale, high luminosity and high coverage ep collisions at a ring–ring LHeC.

Introduction to Transverse Beam Dynamics

This lecture gives an introduction into the design of high-energy storage ring lattices. Applying the formalism that has been established in transverse beam optics, the basic principles of the development of a magnet lattice are explained and the characteristics of the resulting magnet structure are discussed. The periodic assembly of a storage ring cell with its boundary conditions concerning stability and scaling of the beam optics parameters is addressed as well as special lattice insertions such as drifts, mini beta sections, dispersion suppressors, etc. In addition to the exact calculations that are indispensable for a rigorous treatment of the matter, scaling rules are shown and simple rules of thumb are included that enable the lattice designer to do the first estimates and get the basic numbers ‘on the back of an envelope’.

The high luminosity interaction region for a ring?ring Large Hadron Electron Collider

The FCC-hh (Future Hadron-Hadron Circular Collider) is one of the options considered for the next generation accelerator in high-energy physics as recommended by the European Strategy Group. In this overview the status and the evolution of the design of optics integration of FCC-hh are described, focusing on design of the arcs, alternatives, and tuning procedures. LAYOUT OF THE FCC-hh The layout of the FCC-hh ring is shown in Fig. 1. It has only slightly changed compared to the one shown in Ref. [1]. The total circumference of the FCC-hh ring is 97.75 km. The FCC-hh ring is made of 4 short arcs (SAR), 4 long arcs (LAR), 6 long straight sections of 1.4 km (LSS) and 2 extended straight sections of 2.8 km (ESS). The parameters of the ring are given in Table 1. Figure 1: Layout of the FCC-hh ring. The high luminosity interaction points (IPs) are located in the sections LSS-PA and LSS-PG. The value of L∗ in the experimental insertion region (EIR) has been shortened from 45 m to 40 m [2–4], giving a greater flexibility to the optics and reducing the chromaticity generated into the triplet. Two additional IPs (with lower luminosity) are located in the sections LSS-PB and LSS-PL. These sections host the injection as well, which gives additional constraints [2, 4, 5]. The beam H1, which runs in the clockwise direction, is injected into the section LSS-PB and the other one H2 into the section LSS-PL. The RF cavities are located into the section LSS-PH with a beam separation enlarged from 204 mm ∗ Corresponding author: antoine.chance@cea.fr Table 1: Parameters of the FCC-hh Ring Parameter Value Unit Baseline Ultimate Energy 50 TeV Circumference 97.75 km LSS and ESS length 1.4 and 2.8 km SAR and LAR length 3.4 and 16 km β∗ 1.1 0.3 m L∗ 40 m Normalized emittance 2.2 μm γtr 98.806 98.802 Qx/Qy 110.31/ 107.32 Qx/Q y 2/2 Beam separation 204 mm Beam separation (RF) 420 mm to 420 mm. This section is currently made of FODO cells. The extraction section is located in the section ESS-PD and enables the extraction of both beams in the same section [5]. The betatron cleaning section is located in the section ESS-PJ for both beams. The momentum cleaning section is located in the section LSS-PF for both beams [6–8]. UPDATES OF THE ARC CELLS To reduce the cost and to enable the compatibility between FCC-hh and HE-LHC, the beam separation is 204 mm [9,10]. Because of the strong magnetic field in the dipoles, the yoke saturates at collision energy and creates a quadrupole component. The dipoles have then a systematic b2 component, which increases from injection (near 0) to collision energy (near 50 units). Moreover, the sign of b2 is inverted between the inner and outer sides of the arcs for the cos θ or block designs. For the beam H1, we consider then b2 = 50 from PA to PB and from PG to PL and b2 = −50 in the other sections. For the beam H2, the signs are inverted. The integrated quadrupole component in a dipole is given by: b2Ld ρRref ≈ 0.4 × 10−3 (1) where Ld and ρ are respectively the length and the curvature radius of the dipole, Rref = 17 mm is the reference radius. For comparison, the integrated gradient in one arc quadrupole is about 14×10−3. Since there are 12 dipoles and 2 quadrupoles per cell, the integrated gradient in the dipoles is equal to 17% of the one in the main quadrupoles, which is not negligible. That is why the b2 component of the dipoles is not considered as a perturbation and is taken into account 9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW Publishing ISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-MOPMF025 01 Circular and Linear Colliders A01 Hadron Colliders MOPMF025 141 Co nt en tf ro m th is w or k m ay be us ed un de rt he te rm so ft he CC BY 3. 0 lic en ce (© 20 18 ). A ny di str ib ut io n of th is w or k m us tm ai nt ai n at tri bu tio n to th e au th or (s ), tit le of th e w or k, pu bl ish er ,a nd D O I.

Lattice Design in High-Energy Particle Accelerators

This paper gives an overview of the transverse particle dynamics in synchrotrons and storage rings. The main emphasis is on giving an introduction to the basic concepts, described in linear approximation and allowing the reader to deduce the main parameters of a machine, based on some simple scaling laws.

Overview of Arc Optics of FCC-hh

The paper gives an overview of the principles of particle accelerators and their historical development. After introducing the basic concepts, the main emphasis is on sketching the layout of modern storage rings and discussing their limitations in terms of energy and machine performance. Examples of existing machines, among them the Large Hadron Collider (LHC) at CERN, demonstrate the basic principles of and the technical and physical limits that we face in the design and operation of particle colliders. The push for ever higher beam energies motivates the design of future colliders as well as the development of more efficient acceleration techniques.

Transverse Beam Dynamics

The paper gives an overview of the particle dynamics in synchrotrons and storage rings. Both, transverse as well as the longitudinal plane are described in linear approximation. The main emphasis is to give an introduction into the basic concepts and to allow the reader to deduce the main parameters of the machine, based on some simple scaling laws.